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A note on construction of a composite index by optimization of Shapley value shares of the constituent variables

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Abstract

This paper proposes a method to construct composite index, which is a linear combination of several variables, by deriving weights on the criterion of Shapley value (from cooperative game theory) that a constituent variable has in making the composite index. In practice it is found oftentimes that the most common method of principal component analysis has a tendency to ignore (or poorly weigh) those constituent variables that do not have strong correlation with the sister variables. This elitist nature of PCA forces a compromise upon the analyst’s desire and need to incorporate those weakly correlated (but theoretically and practically important) variables into the composite index. In that case, one must construct a composite index that is more inclusive in nature. The Shapley value based composite index meets that requirement.

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  • Mishra, SK, 2016. "A note on construction of a composite index by optimization of Shapley value shares of the constituent variables," MPRA Paper 72330, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:72330
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    References listed on IDEAS

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    1. Michela Nardo & Michaela Saisana & Andrea Saltelli & Stefano Tarantola & Anders Hoffman & Enrico Giovannini, 2005. "Handbook on Constructing Composite Indicators: Methodology and User Guide," OECD Statistics Working Papers 2005/3, OECD Publishing.
    2. Mishra, SK, 2012. "A comparative study of trends in globalization using different synthetic indicators," MPRA Paper 38028, University Library of Munich, Germany.
    3. Sudhanshu K Mishra, 2013. "Global Optimization of Some Difficult Benchmark Functions by Host-Parasite Coevolutionary Algorithm," Economics Bulletin, AccessEcon, vol. 33(1), pages 1-18.
    4. Sudhanshu K. MISHRA, 2016. "Shapley Value Regression and the Resolution of Multicollinearity," Journal of Economics Bibliography, KSP Journals, vol. 3(3), pages 498-515, September.
    5. Mishra, SK, 2007. "A Comparative Study of Various Inclusive Indices and the Index Constructed by the Principal Components Analysis," MPRA Paper 3377, University Library of Munich, Germany.
    6. Noelia Somarriba & Bernardo Pena, 2009. "Synthetic Indicators of Quality of Life in Europe," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 94(1), pages 115-133, October.
    7. Andrea Saltelli, 2007. "Composite Indicators between Analysis and Advocacy," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 81(1), pages 65-77, March.
    8. Mishra, SK, 2008. "On construction of robust composite indices by linear aggregation," MPRA Paper 9232, University Library of Munich, Germany.
    9. José-María Montero & Coro Chasco & Beatriz Larraz, 2010. "Building an environmental quality index for a big city: a spatial interpolation approach combined with a distance indicator," Journal of Geographical Systems, Springer, vol. 12(4), pages 435-459, December.
    10. Mishra, SK, 2007. "Construction of an Index by Maximization of the Sum of its Absolute Correlation Coefficients with the Constituent Variables," MPRA Paper 3333, University Library of Munich, Germany.
    11. Frederik Booysen, 2002. "An Overview and Evaluation of Composite Indices of Development," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 59(2), pages 115-151, August.
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    Cited by:

    1. Sudhanshu K. MISHRA, 2017. "Almost equi-marginal principle based composite index of globalization: China, India and Pakistan," Journal of Economic and Social Thought, KSP Journals, vol. 4(3), pages 335-351, Seprember.
    2. Mishra, SK, 2017. "Are Democratic Regimes Antithetical to Globalization?," MPRA Paper 83321, University Library of Munich, Germany.
    3. Sudhanshu K. MISHRA, 2017. "Measuring degree of globalization of African Countries on almost equimarginal contribution principle," Journal of Economics Bibliography, KSP Journals, vol. 4(4), pages 345-353, December.
    4. Sudhanshu K. MISHRA, 2018. "Globalization under hysteresis: A study of Eastern Bloc Countries, China and India," Journal of Social and Administrative Sciences, KSP Journals, vol. 5(1), pages 46-59, March.
    5. Sudhanshu K. MISHRA, 2017. "Trends in globalization of select Asian countries," Journal of Economic and Social Thought, KSP Journals, vol. 4(4), pages 451-466, December.

    More about this item

    Keywords

    Shapley value; Composite index; Principal Component Analysis; Inclusive indices; Global optimization;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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